If you dig the compost into the soil, it usually disappears evenly. If you apply a layer to the top of the soil, the coarser stuff will last longer and look like this.

It's normal.

To add to that just a teeny bit, being 100% ready to use is not the same as being 100% composted. Compost will pretty much always be highly variable in the size of its pieces. Also, "mulch" is not a stage of decomposition; it's a place to be. Anything can be a mulch: rubber, sand, straw, wood shreds, bones, even highly decomposed compost..

I'm curious to hear how you make compost. I have a chipper-shredder but that does not seem to be the norm on this forum. I incorporate wood chips but allow the compost to age more than a year. I don't get this sort of result.

If you used your compost as mulch, good job! That's where it belongs - on top of the soil, not in the soil. Root activity is just below the surface of the soil and benefits from having that layer of compost above it. If you're going to be applying more compost soon, I'd scrape those wood chips off and then reapply them on top of the compost mulch. They will protect the soil from wind, rain and especially the sun.

My experience is vegetable gardening in clay soil in SW Idaho, alkaline but otherwise fertile soil. What worked best was a layer of compost in contact with the surface of the soil, covered by a mulch. I would dig holes to transplant into, but did not till the soil.

I'm still getting my garden bed going here in SW Washington and the soil is quite different. More silt than clay.